Density Waves Excited by Low-Mass Planets in Protoplanetary Disks I: Linear Regime

Abstract

Density waves excited by planets embedded in protoplanetary disks play a central role in planetary migration and gap opening processes. We carry out 2D shearing sheet simulations to study the linear regime of wave evolution with the grid-based code Athena, and provide detailed comparisons with the theoretical predictions. Low mass planets (down to ~0.03 Earth mass at 1 AU) and high spatial resolution (256 grid points per scale height) are chosen to mitigate the effects of wave nonlinearity. To complement the existing numerical studies, we focus on the primary physical variables such as the spatial profile of the wave, torque density, and the angular momentum flux carried by the wave, instead of secondary quantities such as the planetary migration rate. Our results show percent level agreement with theory in both physical and Fourier space. New phenomena such as the change of the toque density sign far from the planet are discovered and discussed. Also, we explore the effect of the numerical algorithms, and find that a high order of accuracy, high resolution, and an accurate planetary potential are crucial to achieve good agreement with the theory. We find that the use of a too large time-step without properly resolving the dynamical time scale around the planet produces incorrect results, and may lead to spurious gap opening. Global simulations of planet migration and gap opening violating this requirement may be affected by spurious effects resulting in e.g. the incorrect planetary migration rate and gap opening mass.